exact real computer arithmetic



Constructivism, Realizability, Computability



Exact real computer arithmetic refers to treatment of real number arithmetic on computers to finite (necessarily) but arbitrary precision. This is in contrast with what is called floating-point arithmetic? which uses just one fixed finite approximation of the real numbers by natural numbers.

Exact real computer arithmetic essentially implements what in mathematical computability theory is known as the type-II theory (in contrast to the “type-I” theory of partial recursive functions acting just on natural numbers). The formal mathematical definition of computable function (analysis) is the core topic of constructive analysis/exact analysis.


Discussion of implementation of exact real computer arithmetic includes

Discussion relating to computability theory, Type Two Theory of Effectivity and constructive analysis/computable analysis includes

A collection of further references is listed at